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A 2kg 2 kg object is moving in along the x x -axis under a single conservative force. When the object is at position x=0 x = 0 , its speed is 3ms 3 m s . The potential energy U U associated with the conservative force is given as a function of x x by the equation U=αx2 U = α x 2 , where α=4Nm α = 4 N m . Which of the following is correct about the motion of the object?

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Answer:

The particle comes to rest before reaching the position x=4m.

Explanation:

When the object is at x=0m, all of its energy is kinetic energy. Using the equation for kinetic energy yields KE=1/2mv^2=(12)(2)(3)^2=9J. Using the given equation for potential energy when the object is at x=4m yields U=4x^2=4(4)^2=64J. Since the system only has 9J of energy, the object comes to rest before reaching x=4m.

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